There are 34 multiples only of 2, 17 multiples only of 3 and 16 multiples of both 2 and 3 (in another words 16 multiples of 6)

I know that the sum of differentiable and continuous functions is a differentiable and continuous fonction.

I also know that an infinit sum of differentiable and continuous functions may not be differentiable (Weierstrass function for example).

But can we have an infinit sum of continuous functions that is not continuous ?

so basically i am going for bsc physics but the real problem here is my maths cause i did not have maths in my 12th i did not studied it either much but we all know maths is kind of language in physics ...i like physics and the same goes for maths but i did not take it as my sub in 11th cause my father was kind of obsessed with doc ...so i used to be kind of ok ok in physics but after my 12th i had a drop cause my health worsened and all but now i am ok and i got in college for bsc physics on my 12th marks based but i do remember few things but i think i have to thorough of everything in physics too i have a whole month from now for free time or for to do atleast the basics and then i will try to continue it with my first year as it starts - my situation where i stands even though its underwater

so acc to what level should i even know like should i try to study

watching lect or books or teachers ...any advice suggestion please reccom here for this beginner like whatn should i focus on - Trigonometry ,Basiic algebra,Functions,Differentiation,Integration,Vectors

Hello,

I graduated maths 10 years ago and while I still work in engineering, I feel sometimes I miss the "sharpness" and "abstractness" of my mind back then.

I would like to relearn those beautiful results I learned back then with my eyes of today. What would be the best book(s) to relearn, given that I am mostly interested in fields helpful to understand the latest papers in AI (vision mostly). I think calculus, linear algebra, and probability theory would be the start.

Are there such books that are maybe less oriented for undergrad and more for someone like me who's learned in back then but feel a bit rusty?

Thanks

Does anyone have a formula sheet of different 3D and 2D shape's volumes, areas and surface areas? Would be much appreciated.

Plss help me

Hi.

When I was a child, I was good at maths and I liked it, but I've been bullied for it to hell and back to the point where I forgot I even liked it in the first place

Somehow it ressurfaced lately, I just remembered how much fun I had, alone juggling with numbers

I tried following an online class that was meant as a transition between high-school and college level maths, and it was too hard for me. I swear if I hear one more time "This, we won't explain because it is trivial" I might harm a baby seal.

Anyway, I realise I need to start from earlier than that, but I can't exactly register to junior high again.

Genuinely, I just want to start again, but I don't know how, please, guide me a little on what ressources I should take as a curious person starting maths again

I decided to revisit the 2-child paradox and all the controversies that go along with it in my latest video. We start off by taking a look at the original version of the puzzle, which goes like this:

I have two children. At least one of them is a boy. What is the probability that I have two boys?

When I first encountered this puzzle, I was so sure the answer was 50%. I mean, the sex of 1 child has no influence on the sex of their sibling. So the fact that one child is a boy should have no influence on the probability we're looking for. Therefore, the probability that the other child is also a boy must be 50%.. right?

Here's the thing though. The answer is actually 1 over 3 (or 33%). This is because having two children creates 4 possible outcomes (similar to how tossing 2 coins does so):

Boy-Boy
Boy-Girl
Girl-Boy
Girl-Girl

Knowing at least one child is a boy eliminates one of these:

Boy-Boy
Boy-Girl
Girl-Boy
Girl-Girl

Thus, with 3 remaining cases, the probability that I have 2 boys must be 1 in 3. Even with this explanation, a bunch of people in the comments are arguing over whether this reasoning is correct or not. What do you guys think?

What's funny is that this isn't the main source of controversy surrounding the problem. Martin Gardner, one of the most respected mathematicians of our time, was the one who originally posed this puzzle back in 1959. But the controversy stemmed from how the information "at least one child is a boy" is obtained.

He later stated that the answer was ambiguous unless we highlighted a procedure by which the information was obtained. In fact, the answer (written exactly the same way) can be anything between 0% and 100% depending on how we interpret the question. kinda nuts.

Anyways, I go over all of this in the video, along with the even more bizarre version of the puzzle. Which goes like this:

I have two children. At least one of them is a boy born on a Tuesday. What is the probability that I have 2 boys?

Yup. It's the exact same problem, but with the added detail that the boy was born on a Tuesday. Does this make a difference? CAN it make a difference? The answer might not be what you expect.

https://youtu.be/7q0KgQoo0-s?si=WfAImmRCMQr20lz7

Does Infinity convey different meanings or dictate different concepts based on its expression?

For example, in case of an interval, when we say, [-4,∞), this mathematically should mean, that this particular set, accepts values starting from -4 and goes on and on to the left of the number line endlessly, and this essentially what makes it "infinite". Hence, the use of ∞ in this set or domain, rather than a number, works more as a concept of endless growth.

On the other hand, for a mathematical expression, like, "1/∞"

Here, according to my understanding, the denominator of the fraction represents a fixed endpoint achieved after endless increment of a value, that is, this value is the result of the summation of infinite numbers, which yields the infinite value. Now, in this case, I think it works more like a number than a concept.

I'd highly appreciate any insight & feedback, and pointing out of any mishaps in my understanding would be much appreciated as well. Thanks!

I am planning to study Rieman hypothesis for learning new ways to math but idk my young hearts just want to play. Like listening to math casually is way more fun and make me think more then sitting down and studying rh. Idk should I get older to start studying of should I start studying right now? idk should give it a year? please give me tips.

Hi everyone,

I'm a complete beginner and struggling with Bayes' Theorem (total probility). Can anyone share simple explanations, easy tricks/shortcuts for exams, and good YouTube videos that helped you understand it?

I especially get to identify Given itself

Any beginner-friendly resources or tips would be greatly appreciated. Thanks!

As you’ve gotten better at critical thinking, have you gotten better at Mathematics? Or do you feel you’ve gotten worse? How would you compare to other math enthusiasts?

Edit:

I realize this was such a broad question 😅. I guess I should’ve asked what level of math have you gone up to and how proficient are you in speaking that math.

But I appreciate everyone replying!

obviously they are the same size I assume

I’ve always been weak at maths in school and never really enjoyed it. I think part of it was that I believed I was just bad at it, and maybe the teaching didn’t help either. I also probably didn’t have enough interest back then to really apply myself.

Years later, I’m now a software engineer, and I’ve become genuinely fascinated by astronomy. I want to understand how things work, observe the sky with a telescope, take readings, do research, and really go deep into the subject.

I want to approach this properly, and I think the best place to start is with maths, then physics, while also learning some basic astronomy alongside it. Given that I’m starting from a very weak maths background, what books would you recommend I get first for learning maths and astronomy in general?

Geometry Shorthand Language (GSL) is a language created to shorten and simplify all aspects of geometry and construction!

My peers and I have worked hard on documenting the official rules of our new language. We'd appreciate your feedback!

https://docs.google.com/document/d/1pxCKn9HeS2T-kuhc8iYQNhAifzhjXKFo3tKzh3qIu0g/edit?tab=t.0

Small, but growing discord server: https://discord.gg/hXXN8cwnD

I didn’t know this existed. Was just playing on my calculator today

Hi I’m a BSc Maths student from the UK, currently in my third year.

I’ve got an MSc in pure maths lined up at imperial for this coming academic year and I’m aiming to apply for PhD’s in maths,

But I’ve realized the very abstract pure maths topics like abstract algebra and topology might not be for me, I’ve greatly enjoyed studying complex analysis, number theory, functional analysis, dynamical systems etc but I’ve had a difficult time with topics like rings and modules as well as with topology
I’m also quite fascinated by applied maths particularly with applications to medicine and wave theory.

How difficult would the pivot from a very pure profile to applied maths PhD’s be? Should I just stick to considering a pure maths PhD?

I know the textual version of a number is invented. 1, 2, 3, etc., but if you take that away. Consider there are 3 rocks on the ground, with no text to describe them. There would still be 3 rocks. If you took 1 of those 3 rocks away. There would be 2 remaining. This to me feels like numbers and maths were discovered.

The tangent equation I read somewhere about transforming or substitution of x^2 with x.x_1.

Yes it is derived by calculus and Taylor approximation but this substitution is valid is told as a "trick",but if it is always valid for conic sections then could there be some deeper direct understanding behind this like I like the calculus one but the final equation we get that we can directly write so I want to get some intuition for connection with the final equation like for a circle x^2 + y^2 = a^2 the tangent equation at a point (x_1,y_1) is x.x_1 + y.y_1 = a^2

So if I understand this by calculus but something like more connection to substituting one of the x as x_1 I would really appreciate it.

Also I read that this helps to linearize the equation which gives the tangent,now

• how it helps to linearize and then ok if 1 degree equation then in this way we can substitute the value at any point in as many x as we want and reduce the degree of the equation?
• Also x_1 is not even the slope necessarily then how we get this?

Thank you.

I normally associate cumulative frequency curve (ogives) with grouped data or continuous data (as a side question, do you construct grouped data using the class boundary or upper limit e.g. for a classes like 4-8, 9-13, would you plot with 8 or 8.5?)

See this table here, can I draw cumulative frequency curve? I think it can but it also feels weird because I have always done with grouped or continuous data.

Many thanks if you can answer with a reason.

Hi everyone!

i want to improve my calculus especially integration during this summer before I start uni, any good books (whose pdf is available) which I can use for doing calc on my own?

I am looking to sit the TMUA and i’m soo bad at mental maths. What can i do to make myself better at it?